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The Arizona STEM Acceleration Project

Discovering and Calculating Density

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Discovering and Calculating Density

A Secondary Science STEM lesson

Amanda Stalvey

June 22, 2023

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Notes for teachers

  • This lesson is expected to take 2-3 days and is built to act as a phenomena based lab to help students explore and understand density, how to calculate it and why things float.
  • The design for this lesson was taken from the 1st experiment in a chemistry class but could be fit into most general science classes.
  • Students will relate the concepts of mass and volume of various objects to get to the idea of density and comparing the density of several cylinders to water to better understand why things sink or float.

List of Materials

  • Water
  • Scales - Digital or 3-beam balances work
  • Graduated Cylinders
  • Large clear beaker or tub
  • Cylinders of various materials or other objects to be compared that fit into the Graduated Cylinders. FLINN sells a great kit for this - Density Identification Set
  • Glass Stir Rods or other long stick that can help push the cylinders that float into the water for water displacement measurements.

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Science, Math and Engineering Practices

  • plan and carry out investigations
  • analyze and interpret data
  • use mathematics and computational thinking
  • construct explanations and design solutions
  • engage in argument from evidence
  • obtain, evaluate, and communicate information

Core Ideas for Science

U1: Scientists explain phenomena using evidence obtained from observations and or scientific investigations. Evidence may lead to developing models and or theories to make sense of phenomena. As new evidence is discovered, models and theories can be revised.

U2: The knowledge produced by science is used in engineering and technologies to solve problems and/or create products.

Essential HS.P1U1.1

Develop and use models to explain the relationship of the structure of atoms to patterns and properties observed within the Periodic Table and describe how these models are revised with new evidence.

Plus HS+C.P1U1.5

Plan and carry out investigations to test predictions of the outcomes of various reactions, based on patterns of physical and chemical properties.

Plus HS+E.E2U1.13

Analyze and interpret data showing how gravitational forces are influenced by mass, and the distance between objects.

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Objectives:

  • Use water displacement to solve for the volume of different substances.
  • Conduct an experiment using laboratory equipment to learn about the equipment and how it is used properly in the lab.
  • Conduct an experiment to discover the properties of matter, specifically density and how it can be used to identify various substances through laboratory practices.
  • Compare the density of various materials to that of water to explain why some things float and others sink in water.
  • Calculate and apply the concepts of density to the properties of matter.
  • Use a mass over volume graph to plot the densities of different materials and read that graph to understand what will float and what will sink and rank the densities of those materials.

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Agenda - Day 1 “Intro and Planning”

  • Using a large clear tub/beaker of water, students will start by observing items sinking and floating in water as a demonstration. Students should make as many observations about the objects as they can and share them as a class. (5 min)
  • Have students discuss, with seat partners or as a whole class, the properties of matter that determine if a substance will float or sink in water. This discussion should include what data they could collect in the lab to define this. (Students should have some prior knowledge of this from previous classes.) (10 min)
  • Assign groups for the lab and have students design their own experiment and plan to test what the composition of the objects are, as well as the water itself to understand why these objects sink or float (aiming for mass and volume data). (20-30 min)
  • During their planning time each group should:
    • Develop a step process protocol with materials for this.
    • Discuss and design what their data tables should look like and what data they need to collect.
    • The instructor should give students a list of materials that will be available for the lab and discuss any formatting details they would like students to use for the lab assessment. (This could be a lab report.)
  • Closing - The teacher should summarize what was done in class and ask students what they observed and if they achieved their objectives for the day.
    • Before students leave, they should present their protocols to the teacher to be approved for the next day.

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Agenda - Day 2 “Lab Investigation”

  • A review of the objectives of the lab and any safety precautions that students should be aware of prior to releasing to the lab. (5 min)
    • If using glassware in a chemistry lab, students should be wearing goggles per FLINN Safety and lab regulations.
  • Once each group’s protocol and plan for the lab has been checked by the teacher for any flags or concerns, students should be released into the lab to collect data and carry out their lab. (35-45 min)
    • Students should collect data on the water and 3-4 different materials.
  • Suggested Data for students to collect:
    • Mass of each object using a scale.
    • Volume of the objects using water displacement in a graduated cylinder.
      • Students can use a glass stir rod, rubber policeman or other long tool to push buoyant objects down to be level with the meniscus of the water for their volume.
    • Mass of a specific volume of water.
    • Qualitative visual data for each object. (Color, ID code, texture, etc.)
  • Closing - teacher should review the objectives for the day and have students discuss if those objectives were achieved.
    • Possibly assign analysis questions at the end of class for homework or when students complete the data collection.

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Agenda - Day 3 “Analysis and Concept Application”

  • Students should analyze the data they have to relate each object's mass and volume to how it floats or sinks.
  • As a class, students should discuss what the mass of any of their substances would be with zero volume. (0g)
  • Students should plot their lab data on a graph as mass vs. volume with a best fit line connecting to 0 volume and 0 mass, and analyze this graph for all objects compared to the water.
  • As a class, all groups should plot their mass vs. volume data on a shared graph with best fit lines connecting to 0g and 0mL.
    • There should be multiple data points for each object as each group will have overlaps with others.
    • Have students compare their results with those groups since they should be the same.
  • As a class, students should discuss what mass and volume relate to and how it relates to density.
  • Students should calculate the density of the water and plot this as well, if they hadn’t already.
    • In chemistry, this density can be used for various labs.
  • Students should then discuss what density is and how it relates to how compact the matter of an object is in a volume.
  • Students should relate that the greater the mass in a small volume the more dense the object is.
  • As a class, students should then try and identify the different materials used based on this density.
    • Density is a property of matter that can be used to determine the identity of a substance.
  • All of this should take a full 55 min class period.

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What property(ies) of matter determines whether an object will sink or float in water?

Students will begin by observing several different objects of different material placed in water and how some of them float and some sink.

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Hands-on Activity Instructions

  • Students should work in groups of 2-4, to make 10-12 different groups..

Procedure:

  1. Obtain the following materials:
    1. 50mL graduated cylinder
    2. 1 lab testing rod to begin with from the instructor
  2. Scales will be out and set up for use. Make sure to use the same scale for all measurements!
  3. Find and record the mass of the rod.
  4. Take Qualitative Data for which rod ID you have, what the color is, the texture and type of material it is.
  5. Using the graduated cylinder, find the volume of the rod. Record this. (Hint: you may consider using water for this step and ensure the rod is either below the surface of the water or pushed down to be even with the bottom of the meniscus.)
  6. Trade your rod with another group and repeat steps 3-5 for the new rod.
  7. Trade 1-2 more times and repeat steps 3-5 for a each rod.
  8. Return your materials to where you got them; make sure your lab area looks exactly how it was when you got there.
  9. Sit down and start analyzing your data with your group.

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Post-Lab Questions:

Suggested Analysis Questions:

  1. Calculate the volume for each rod using the concepts of water displacement. (How much did the water level change?) Don’t forget to show your work and include units in each answer!
  2. Using a graphing program or graph paper, graph the mass over volume for each rod. This is an x/y-axis graph where x is the volume and y is the mass. These should be dots to begin with!
  3. Assuming the fact that anything with a volume of zero, would have a mass of zero. Draw a best fit line through each data point connecting it to zero. You should now have a line for each rod that should connect to 0,0 for all lines.
  4. Graph the mass over volume for your water data and also draw a line connecting it to 0,0.
  5. Look at which boxes floated and which sank. Where on the graph did they end up compared to the water?
  6. Calculate the density for each rod and the water. Don’t forget to show your work and include units in each answer! Density = mass/volume
  7. Identify each mystery rod from your data using the density table given in class. Cite data to support your answers!!!
  8. Does your answer for #5 make sense based on what you know about density and the identity you made for that block in question #7?

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Density Key for FLINN Kit

Have a table handout for students based on the materials you provide. This is taken from FLINN’s Density Identification Kit Key.

The following are the densities of the included items in ascending order. The densities of the materials may be less consistent than implied by the number of significant figures given. This is particularly true of the wood samples, which may readily vary by 0.06 from the values given. All values are in units of g/cm3. For this lab, some conversions might be needed, but these numbers are close enough for identification.

0.64 g/cm3

Walnut

1.15 g/cm3

Polyamide (Nylon)

1.42 g/cm3

Acetyl

0.75 g/cm3

Oak

1.17 g/cm3

Acrylic

2.2 g/cm3

PTFE (Teflon)

0.77 g/cm3

Maple

1.23 g/cm3

Polyurethane

2.71 g/cm3

Aluminum

0.90 g/cm3

Polypropylene

1.32 g/cm3

Phenolic

8.56 g/cm3

Brass

0.92 g/cm3

Polyethylene (LDPE)

1.37 g/cm3

Polyvinylchloride (PVC)

8.91 g/cm3

Copper

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Assessment

  • Class discussion
  • Formal Lab Report - Analysis Questions
  • Formative Assessment Practice Problems - Graphing Mass vs Volume Practice Worksheet

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Differentiation

The University of Colorado Boulder has a great PhET Simulation for Density that can be done from home. It has a couple limitations but it does allow students to engage in Mass vs. Volume testing.

Remediation - Online Option

Extension/Enrichment

This lab could be replicated with other chemistry lab solids that do not react with water. Students can identify several different elemental solids using this method, specifically gold, aluminum, silver, iron, magnesium, etc.

Or students can do this with liquids as well. Isopropyl alcohol, water, oil, and other homogeneous liquids to better understand properties of matter.